In a vibrating beam accelerometer, a proof mass is mounted to a support by a flexure hinge or the like, and a vibrating beam force transducer is connected along the accelerometer's sensitive axis between the proof mass and the support. An acceleration along the sensitive axis results in a compression or tension force on the force transducer. This force is converted into an electrical signal that indicates both the direction and magnitude of the acceleration. A well-known type of vibrating beam force transducer comprises a quartz crystal arranged as a double-ended tuning fork. The double-ended tuning fork includes a pair of side-by-side beams that are caused to vibrate in a transverse oscillation mode in which the two beams move in their common plane 180.degree. out of phase with one another. Tension or compression forces on the force transducer result in an increase or decrease respectively of the vibration frequency.
Vibrating beam accelerometers possess a number of significant advantages, including excellent scale factor stability. Many error sources in such accelerometers can be greatly reduced by using two proof masses and two sensing crystals operated in a push-pull configuration, such that one crystal is put in compression while the other is put in tension. The output is treated as some function of the frequency difference. This method of measurement cancels out many common mode errors, including the contribution of force crystal nonlinearity to the vibration rectification coefficient. However, a disadvantage of using dual proof masses is that identity of the dynamic responses of the two accelerometers is difficult to achieve. To avoid these problems, it has previously been proposed to use a single proof mass in connection with a pair of force transducers, with the force transducers being connected to the proof mass in the push-pull mode in which one crystal is placed in tension and the other in compression for a given input acceleration. As with the dual proof mass approach, this arrangement may be used to cancel various common mode errors.
A primary source of common mode errors in most vibrating beam accelerometers is related to mismatched coefficients of thermal expansion. Crystalline quartz, in the crystalline axis orientation commonly used for force transducers, has a relatively nonlinear expansion coefficient as a function of temperature. It is extremely difficult to find metals with the proper qualities for flexures which also match the thermal expansion of crystalline quartz. Even if a perfect match were made at a given temperature, the nonlinearities of crystalline quartz expansion would cause mismatches to occur at the operating temperature extremes. Furthermore, it is common for the zero stress point of crystal attachment to be at a temperature substantially above the accelerometer operating range. This is typical for epoxies, anodic bonding, brazing, and glass frit bonding. Thus the resulting accelerometer will have thermal expansion mismatch that will cause common mode stress on the crystals.
Residual stresses on the crystals and mechanism can cause many problems. These problems include high bond line stresses on the end attachment joint, stress on mechanical parts, and stress on crystals. The high bond line stress results in accelerated creep, higher strength requirements, and limitations on usable bonding technologies. Stress on mechanism parts results in reduced shock load capability, dimensional instability, and additional strength requirements. Stress on the crystals results in dimensional instabilities, reduced full range capability, changes in crystal operating points, higher temperature sensitivities, and differential mode errors due to unequal stiffness.